Beta, the Clopper-Pearson exact interval has coverage at least 1-alpha,
but is in general conservative. Most of the other methods have average
coverage equal to 1-alpha, but will have smaller coverage in some cases.

The ‘beta’ and ‘jeffreys’ interval are central, they use alpha/2 in each
tail, and alpha is not adjusted at the boundaries. In the extreme case
when count is zero or equal to nobs, then the coverage will be only
1 - alpha/2 in the case of ‘beta’.

The confidence intervals are clipped to be in the [0, 1] interval in the
case of ‘normal’ and ‘agresti_coull’.

Method “binom_test” directly inverts the binomial test in scipy.stats.
which has discrete steps.